Complex Bandpass Filter Design

This example shows how to design complex bandpass filters. Complex bandpass filters are used in many applications from IF subsampling digital down converters to vestigial sideband modulation schemes for analog and digital television broadcast. One easy way to design a complex bandpass filter is to start with a lowpass prototype and apply a complex shift frequency transformation. In this example, we review several cases of lowpass prototypes from single-stage single-rate FIR filters to multistage multirate FIR filters to IIR filters.

Single-Stage Single-Rate FIR Design

In the case of a single-rate FIR design, we simply multiply each set of coefficients by (aka 'heterodyne with') a complex exponential. In the next example, we rotate the zeros of the lowpass Nyquist filter prototype by a normalized frequency of .6.

Multirate Multistage FIR Design

In the case of multirate multistage FIR filters, we need to account for the different relative frequencies each filter operates on. In the case of a multistage decimator, the desired frequency shift applies only to the first stage. Subsequent stages must also scale the desired frequency shift by their respective cumulative decimation factor.

Similarly, in the case of a multistage interpolator, the desired frequency shift applies only to the last stage. Previous stages must also scale the desired frequency shift by their respective cumulative interpolation factor.

Single-Rate IIR Design

Finally in case of single-rate IIR designs, we can either use a complex shift frequency transformation or a lowpass to complex bandpass IIR transformation. In the latter case, the bandwidth of the bandpass filter may also be modified.